what are the domain and range of the function f(x) = 3^x + 5?\no domain: (-∞, ∞); range: (0, ∞)\no domain…

what are the domain and range of the function f(x) = 3^x + 5?\no domain: (-∞, ∞); range: (0, ∞)\no domain: (-∞, ∞); range: (5, ∞)\no domain: (0, ∞); range: (-∞, ∞)\no domain: (5, ∞); range: (-∞, ∞)

what are the domain and range of the function f(x) = 3^x + 5?\no domain: (-∞, ∞); range: (0, ∞)\no domain: (-∞, ∞); range: (5, ∞)\no domain: (0, ∞); range: (-∞, ∞)\no domain: (5, ∞); range: (-∞, ∞)

Answer

Explanation:

Step1: Determine the domain of a linear function

For a linear function (y = 3x+5), there are no restrictions on the value of (x). So the domain is all real numbers, which is written in interval notation as ((-\infty,\infty)).

Step2: Determine the range of a linear function

Since the function (y = 3x + 5) is a straight - line (linear) function with a non - zero slope ((m = 3)), it can take on any real number value. If we solve for (x) in terms of (y) ((x=\frac{y - 5}{3})), there are no restrictions on (y). So the range is also all real numbers, written as ((-\infty,\infty)).

Answer:

domain: ((-\infty,\infty)); range: ((-\infty,\infty))